A058075 Numbers k such that gcd(sigma(k), sigma(k+1)) = 1, where sigma(k) is sum of positive divisors of k.
1, 2, 3, 4, 7, 8, 9, 15, 16, 18, 24, 25, 31, 35, 36, 48, 63, 64, 72, 80, 81, 97, 99, 100, 120, 121, 127, 128, 143, 144, 162, 200, 224, 225, 241, 255, 256, 288, 289, 323, 337, 399, 400, 483, 511, 512, 528, 529, 575, 576, 577, 578, 624, 625, 675, 721, 722, 728, 729
Offset: 1
Keywords
Examples
8 is included because sigma(8) = 15 is relatively prime to sigma(9) = 13.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..3000 from Ivan Neretin)
Crossrefs
Cf. A058074.
Programs
-
Mathematica
Select[Range@800, GCD @@ DivisorSigma[1, {#, # + 1}] == 1 &] (* Ivan Neretin, Jan 27 2017 *) Drop[Position[Partition[DivisorSigma[1,Range[800]],2,1],?(GCD@@#== 1&)]// Flatten,2] (* _Harvey P. Dale, Jul 31 2019 *) -
PARI
lista(nn) = {for(n=1, nn, if (gcd(sigma(n), sigma(n+1)) == 1, print1(n, ", ")));} \\ Michel Marcus, May 19 2014